Allometric Theory Explains Self‐Thinning Relationships of Mountain Beech and Red Pine

Allometric theory on mechanisms of the self—thinning rule was tested for Nothofagus solandri populations from the Craigieburn Range, New Zealand and for Pinus densiflora stands from northern Japan. The self—thinning rule describes a consistent relationship of mean plant mass to the approximately —3/2 power of plant density in evenaged monocultures. Although his rule has been described for various species, mechanisms that produce certain relationships have not been well understood. We tested an allometric theory of Long and Smith of the self—thinning rule that assumes constant foliage mass density and allometry for mean dimensions of populations that represent dense conditions for given mean plant sizes. Only stands at maximum crowding were selected for analysis. The self—thinning boundary of N. solandri showed an exponent —1.13 with a 95% ci of —1.25 to —1.02 for mean stem mass. This was significantly shallower than the conventional value of the exponent —3/2, but was identical to the predicted exponent from the allometric theory. The thinning coefficient was also explained numerically by this hypothesis. In contrast, analysis of published data for P. densiflora indicated that the thinning exponent did not differ from the proposed —3/2. Empirical thinning lines varied substantially depending on species and plant parts considered; however, the allometric theory consistently provided predictions that agreed with the observed thinning relationships. Implications for the geometry of self—thinning populations and generality of the allometric theory are discussed.